Kindly suggest the procedure of fitting creep data and recovery data using LSQ if the constitutive equations for both creep and recovery data are known.
Thanks
Vivek
Dear Vivek,
For that purpose, you could use Matlab (or an equivalent open source code like Octave); particularly, the Matlab command termed “nlinfit”:
b = nlinfit (X, y, @fun, b0)
This command returns a p-by-1 vector b of coefficient estimates for nonlinear regression of responses in y on predictors in X using a model specified by fun.
That is, X would be for example the n-by-1 vector with the instants of time in which you recorded creep strain data, and y would be the n-by-1 vector of those values of creep strain measured experimentally. Then, fun is the function handle where you specify the model or the constitutive equations that you want to fit to the creep strain experimental data. For instance, for creep, in fun you could use the θ Projection Concept or θ Methodology [1,2,3,4]. This set of equations have four fitting parameters: θ1, θ2, θ3, and θ4. Hence, the vector b returned by nlinfit would be a 4-by-1 vector with the fitted values of θ1, θ2, θ3, and θ4. Before executing nlinfit, you should provide also b0, a 4-by-1 vector with given initial values to the fitted parameter, for the code to be able to start the fitting procedure.
Hope this helps,
Jose
[1] Evans, R. W., & Wilshire, B. (1996). Constitutive Laws for High-Temperature Creep and Creep Fracture. In A. S. Krausz & K. Krausz (Eds.), Unified Constitutive Laws of Plastic Deformation (Vol. 1, pp. 107–152). San Diego, CA, USA: Academic Press, Inc.
[2] Burt, H., & Wilshire, B. (2004). Theoretical and practical implications of creep curve shape analyses for 2124 and 2419. Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science, 35A(6). doi:10.1007/s11661-004-0078-8
[3] Burt, H., & Wilshire, B. (2005). Theoretical and practical implications of creep curve shape analyses for 8090. Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science, 36A(5). doi:10.1007/s11661-005-0214-0
[4] Burt, H., & Wilshire, B. (2006). Theoretical and practical implications of creep curve shape analyses for 7010 and 7075. Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science, 37A(3A), 1005–1015.
- Badges
- Science topic
- Similar topics
- Social Psychology
- Attitude